IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v13y2007i6p523-544.html
   My bibliography  Save this article

Skew Brownian Motion and Pricing European Options

Author

Listed:
  • T. R. A. Corns
  • S. E. Satchell

Abstract

The volatility smile and systematic mispricing of the Black-Scholes option pricing model are the typical motivation for examining stochastic processes other than geometric Brownian motion to describe the underlying stock price. In this paper a new stochastic process is presented, which is a special case of the skew-Brownian motion of Ito and McKean. The process in question is the sum of a standard Brownian motion and an independent reflecting Brownian motion that is similar in construction to the stochastic representation of a skew-normal random variable. This stochastic process is taken in its exponential form to price European options. The derived option price nests the Black-Scholes equation as a special case and is flexible enough to accommodate stochastic volatility as well as stochastic skewness.

Suggested Citation

  • T. R. A. Corns & S. E. Satchell, 2007. "Skew Brownian Motion and Pricing European Options," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 523-544.
    • Handle: RePEc:taf:eurjfi:v:13:y:2007:i:6:p:523-544
    DOI: 10.1080/13518470701201488
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13518470701201488
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/13518470701201488?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaoyang Zhuo & Olivier Menoukeu-Pamen, 2017. "Efficient Piecewise Trees For The Generalized Skew Vasicek Model With Discontinuous Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-34, June.
    2. Marco Minozzo, 2011. "On the existence of some skew normal stationary processes," Working Papers 20/2011, University of Verona, Department of Economics.
    3. Hussain, Sultan & Arif, Hifsa & Noorullah, Muhammad & Pantelous, Athanasios A., 2023. "Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    4. Yizhou Bai & Zhiyu Guo, 2019. "An Empirical Investigation to the “Skew” Phenomenon in Stock Index Markets: Evidence from the Nikkei 225 and Others," Sustainability, MDPI, vol. 11(24), pages 1-17, December.
    5. Song, Shiyu & Wang, Suxin & Wang, Yongjin, 2015. "First hitting times for doubly skewed Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 212-222.
    6. Pasricha, Puneet & He, Xin-Jiang, 2022. "Skew-Brownian motion and pricing European exchange options," International Review of Financial Analysis, Elsevier, vol. 82(C).
    7. Che Guo & Xingchun Wang, 2022. "Pricing vulnerable options under correlated skew Brownian motions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 852-867, May.
    8. Yuan Hu & Abootaleb Shirvani & W. Brent Lindquist & Frank J. Fabozzi & Svetlozar T. Rachev, 2021. "Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis," Papers 2106.09128, arXiv.org.
    9. Svetlozar Rachev & Nancy Asare Nyarko & Blessing Omotade & Peter Yegon, 2023. "Bachelier's Market Model for ESG Asset Pricing," Papers 2306.04158, arXiv.org.
    10. Rossello, Damiano, 2012. "Arbitrage in skew Brownian motion models," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 50-56.
    11. Tian, Yingxu & Zhang, Haoyan, 2018. "Skew CIR process, conditional characteristic function, moments and bond pricing," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 230-238.
    12. Jun Maeda & Saul D. Jacka, 2017. "An Optimal Stopping Problem Modeling Technical Analysis," Papers 1707.05253, arXiv.org, revised Mar 2020.
    13. Hu, Yuan & Lindquist, W. Brent & Rachev, Svetlozar T. & Shirvani, Abootaleb & Fabozzi, Frank J., 2022. "Market complete option valuation using a Jarrow-Rudd pricing tree with skewness and kurtosis," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    14. Mahdi Doostparast, 2017. "Explicit expressions for European option pricing under a generalized skew normal distribution," Papers 1707.09609, arXiv.org.
    15. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
    16. Luis H. R. Alvarez E. & Paavo Salminen, 2017. "Timing in the presence of directional predictability: optimal stopping of skew Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 377-400, October.
    17. J. A. Jiménez & V. Arunachalam & G. M. Serna, 2015. "Option Pricing Based On A Log–Skew–Normal Mixture," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-22, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:eurjfi:v:13:y:2007:i:6:p:523-544. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.